Ion-exchange or ion-selective membranes are semi-permeable membranes that transport certain dissolved ions, while blocking other ions or neutral molecules. Such membranes typically comprise an organic or inorganic polymer with charged (ionic) side groups to control ion transport. Ion-selective membranes are often used in electrodialysis, having applications in seawater desalination, industrial wastewater treatment of highly scaling waters, food and beverage production, and other industrial wastewaters. Electrodialysis uses ion-selective membranes to transport salt (MX) or acid from one solution, the diluate, to another solution, the concentrate, by applying an electric current. A convention electrodialysis cell is shown in FIG. 1. The cell comprises a diluate compartment and a concentrate compartment formed by an anion exchange membrane (AEM) and cation exchange membranes (CEM) placed in an electrolyte between two electrodes. The feed or diluate stream, concentrate or brine stream, and electrode (anolyte and catholyte) streams are allowed to flow through the appropriate cell compartments formed by the ion-selective membranes. Under the influence of an electrical potential difference, the negatively charged anions (X−) in the feed or diluate stream migrate toward the positively charged anode. These anions pass through the positively charged AEM, but are prevented from further migration toward the anode by the negatively charged CEM and therefore stay in the concentrate stream, which becomes concentrated with the anions. The positively charged cations (M+) in the feed or diluate stream migrate toward the negatively charged cathode and pass through the negatively charged CEM. Cations in the concentrate stream are prevented from further migration toward the cathode by the positively charged AEM. As a result of the anion and cation migration, electric current flows between the cathode and anode. The overall result of the electrodialysis process is a depletion in the salt content in the diluate compartment and an enrichment in the salt content in the concentrate compartment. In almost all practical electrodialysis processes, multiple electrodialysis cells are arranged into a configuration called an electrodialysis stack, with alternating anion and cation exchange membranes forming the multiple electrodialysis cells.
Ion-selective nanoporous membranes offer a convenient platform with which to control ion transport. See C. R. Martin et al., Adv. Mater. 13, 1351 (2001). The relative ratio of pore surface area to electrolyte volume provides an opportunity to tune ion transport through the pore by controlling surface charge on the pore wall. See W. Guo et al., Chem. Res. 46, 2834 (2013); and H. Daiguji, Chem. Soc. Rev. 39, 901 (2010). In this respect, many groups have successfully leveraged a variety of responsive chemistries to alter the surface charge, and resulting ion transport, through a nanoporous membrane. See J. Elbert et al., Adv. Funct. Mater. 24, 1591 (2014); Q. Zhang et al., Adv. Funct. Mater. 24, 424 (2014); T. Liu et al., Chem. Commun. 49, 10311 (2013); I. Vlassiouk et al., Nano. Lett. 6, 1013 (2006); F. Buyukserin et al., Small 3, 266 (2007); and L. J. Small et al., Nanoscale 7, 16909 (2015). Moreover, different ion transport behavior can be achieved through control of the nanopore shape, for example cones can give rise to different degrees of ion rectifying behaviors normally absent in simple cylindrical nanopores, important factors for overall control of ion transport in the membranes. See P. Apel et al., Nucl. Instrum. Meth. B 184, 337 (2001); N. Li et al., Anal. Chem. 76, 2025 (2004); L. J. Small et al., RSC Adv. 4, 5499 (2014); J. Cervera et al., J. Chem. Phys. 124, 104706 (2006); Z. Siwy et al., J. Am. Chem. Soc. 126, 10850 (2004); and C. Kubeil and A. Bund, J. Phys. Chem. C 115, 7866 (2011).